James and Rupert Murdoch before the culture, media and sport select committee last July. They are likely to be called to the Leveson inquiry alongside other newspaper owners, as well as Rebekah Brooks, David Cameron and Tony Blair. Photograph: PA

Rupert Murdoch and James Murdoch are expected to appear at the inquiry into press ethics within weeks after Lord Justice Leveson announced he would be calling in newspaper owners to give evidence between now and the middle of May.

Lord Rothermere, owner of Daily Mail publisher Associated Newspapers, is also expected to be asked to testify under oath.

So too is Eygeny Lebedev, the son of the Russian proprietor of the Evening Standard, Independent and the cut-price i. It is believed all three proprietors have been pencilled in for the week beginning 23 April.

Aidan Barclay the son of media-shy Sir David Barclay - who with his brother and Sir Frederick owns the Daily Telegraph and Sunday Telegraph - is also to be called.

The newspaper owners are expected to be grilled about their relationship with politicians including David Cameron and past prime ministers Tony Blair and Gordon Brown, including details of their specific meetings, correspondence and telephone calls.

Rebekah Brooks, the former chief executive of News International, has been confirmed as a witness for the next module of the inquiry which is examining the relationships between the press and politicians.

Tom Watson, the Labour MP who led the calls for an investigation into phone hacking, has applied to be a core particpant in the next stage of the inquiry as has Brooks and Evan Harris, the former Liberal Democrat MP who advised the Hacked Off campaign for an inquiry into press standards last July.

David Cameron, Tony Blair and Gordon Brown will also be called before Leveson, who is expected to discuss their relationship with the Murdochs, Rothermeres and Barclays in the runup to general elections.

Leveson did not mention the Murdochs by name, however their appearance will generate worldwide interest.

The last time Murdoch and his youngest son James appeared in front of British authorities was in July when they were summoned to answer questions at a parliamentary committee investigating phone hacking.

In an extraordinary day of testimony, Rupert Murdoch declared it "the most humble day of my life" and told MPs how sorry they were to the victims of the News of the World phone hacking.

Newspaper owners will give evidence over two weeks.

"During the week commencing 23 April, I apprehend that we will be calling some proprietors or media owners and other evidence crossing modules," said Leveson. He said more proprietors would be summoned on the week commencing 8 May.

That week Leveson will return to the Guardian's story last July about voicemail interceptions of the murdered teenager Milly Dowler that led to a public outrage over phone hacking which prompted the closure of the News of the World.

The Guardian reported that the murdered school girl's phone had been hacked and her voicemails deleted by News of the World, giving rise to a "false hope" moment for her distraught parents.

It has since emerged that the voicemails may have been deleted automatically by the telephone companies. Surrey Police are investigating the matter and told Leveson that it will submit its findings to the inquiry at the end of May.

Leveson said on Tuesday that the time was coming to "simply draw a line" under the matter which he will return to on the week beginning 8 May.

• This article was corrected on 4 April 2012 because it said that Aidan Barclay was "son of Sir David and Sir Frederick Barclay".